Subspace-based method for joint range and DOA estimation of multiple near-field sources

doi:10.1016/j.sigpro.2006.01.015

Signal Processing

Volume 86, Issue 8, August 2006, Pages 2129-2133

https://doi.org/10.1016/j.sigpro.2006.01.015 Get rights and content

Abstract

A subspace-based method for joint range and DOA (direction-of-arrival) estimation of multiple near-field sources is presented. The proposed method uses fourth-order cumulants, and the range and DOA parameters are directly given by the eigenvectors and eigenvalues of a constructed matrix. Compared with some available methods, the 2D parameters are automatically paired and the loss of array aperture is also reduced. Performance evaluation via computer simulations is included to demonstrate the effectiveness of the proposed algorithm.

Introduction

Direction-of-arrival (DOA) estimation is an important research problem in radar, sonar, radio-astronomy, communication, etc, and many classical algorithms have been developed under the assumption of far-field sources, such as Capon, ML (maximum likelihood), MUSIC, ESPRIT [1], etc. When the source is in the Fresnel field of array aperture, however, the plane wavefront approximation to the spherical wavefront is no longer valid and leads to a performance degradation of previous classical algorithm in the presence of near-field sources [2], [3], [4], [5], [6], [7]. In recent years, many bearing estimation methods for near-field source have been proposed in the literature, including ML [2], 2D MUSIC [3], [4], ESPRIT-like based on high-order statistics [5], WLP [6] (weighted linear prediction), 1D MUSIC [7], etc. Most of methods proposed in the above literature need multiple-dimension search computation or additional parameters pairing processing, in addition, several existing methods [5], [6] without search computation load need use the symmetric structure of array and hence the effective aperture of array is largely reduced.

To overcome the shortcomings aforementioned, in this paper, we introduce a new method for joint range and DOA estimation of multiple narrow-band near-field sources. The proposed method uses the fourth-order cumulants, and the ranges and DOAs parameters are directly obtained from the eigenvectors and eigenvalues of the eigen-decomposition of a constructed matrix. Compared with some available methods [5], [6], the advantages of the proposed method lie in that the 2D parameters pairing is not required and the loss of array aperture is also effectively avoided(see Table 1 for comparison).

Section snippets

Proposed method

Consider an uniform linear array of $N$ sensors with inter-element spacing $d$ , assumes that $P$ narrow-band near-field signals impinge on the array. The output of the $m$ th sensor can be approximately expressed by (see [5], [6] for details) $x_{m} (t) = \sum_{i = 1}^{P} s_{i} (t) e^{j (ω_{i} m + φ_{i} m^{2})} + n_{m} (t) for m = - 1, 0, 1, \dots, N - 2 .$ The parameters $ω_{i}$ and $φ_{i}$ are functions of the azimuth $θ_{i}$ and range $r_{i}$ of the $i$ th source, and they are expressed as $ω_{i} = \frac{- 2 π}{λ} d \sin (θ_{i}) and φ_{i} = π \frac{d^{2}}{λ r_{i}} \cos^{2} (θ_{i})$ For unique estimation of source parameters, the following

Simulation results

To verify the performance of the proposed method, a set of computer simulations is carried out in this section. We consider a uniform linear array consisting of $n = 6$ antennas with inter-spacing $d = λ / 4$ . The reference sensor is sensor 0. Two equal power uncorrelated signal sources imping on this array. The estimation performance is measured by the root mean square error(RMSE). The RMSE of range parameter is normalized by the signal wavelength $λ$ . All results provided were averages of 500 independent

Conclusions

A novel subspace-based method is presented for localization of multiple near-field sources. The proposed algorithm uses effectively the aperture of array, and hence our method can estimate the DOAs of $N - 1$ signal sources using N sensors. The proposed algorithm does not need to search computation and parameters pairing processing. Furthermore, the simulation results are included to demonstrate the performance improvement of the proposed algorithm compared to the existing ESPRIT-like method.

Acknowledgments

The work described in this paper was supported in part by the National Nature Science Foundation of China (Project no.60302006 and no.60462002).

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Direction-of-arrival (DOA) estimation in near-field is one important research topic, and most relevant algorithms [1–5] have been proposed generally based on the assumption of point sources.
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Fast communicationSubspace-based method for joint range and DOA estimation of multiple near-field sources

Abstract

Introduction

Section snippets

Proposed method

Simulation results

Conclusions

Acknowledgments

Two decades of array processing research: the parametric approach

IEEE Signal Process. Mag.

Near-field multiple sources localization by passive sensor array

IEEE Trans. Antennas Propag.

Fast communication
Subspace-based method for joint range and DOA estimation of multiple near-field sources